# Would dark matter absorb gravitational waves?

Would the vast and seemingly diffuse clouds of dark matter floating around our galaxy (and most others) absorb gravitational waves? Is this perhaps why we haven't detected any yet?

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If DM absorbed gravity waves, maybe the energy gained would be detected via very low frequency radiation from increases in temperature. –  Michael Luciuk May 20 '11 at 20:53
The cross section for absorption would be very small unless there is some special way for dark matter to couple to gravity (which would make it much, much more mysterious than it already is). I'll look up a reference or write something up when I have more time, but the answer here is very close to 'no' –  Jerry Schirmer May 20 '11 at 20:55
@Jerry Schirmer: Thanks. It was just a random thought that occurred to me, and struck me as a question that physicists may not have thought of yet. I figured they probably had. –  Omnifarious May 20 '11 at 22:06
@Michael Luciuk: Well if dark matter really is dark (which there all indications that it is), it wouldn't have any way to re-radiate the energy except through gravity waves of its own. I think one of the reasons its posited that dark matter can't coalesce into larger aggregations is because it has no way to radiate energy, and so can't really slow down. –  Omnifarious May 20 '11 at 22:08
@Michael Luciuk: Its temperature would increase, and that would result in dark matter moving at an average higher velocity. Thinking about it, that's likely inconsistent with the fact that dark matter appears loosely clumped around galaxies. It still has most of the energy it had at the big bang, but if it had sucked up more from gravity waves, it would probably have too much for even the diffuse cloud that now exists. It would likely have dispersed a lot more evenly throughout the universe. –  Omnifarious May 20 '11 at 22:35

It is very difficult to detect gravitational waves because gravity is such a weak force. For the same reason though it's very difficult to dampen gravitational waves. We know that dark matter behaves similar to 'normal matter' for what its equation of state and coupling is concerned, so it won't be able to absorb gravitational waves any more efficiently, which is essentially not at all. (Also: The expression 'gravity waves' describes a phenomenon seen in cloud formation and has nothing to do with General Relativity as Google will tell you.)

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""We know that dark matter behaves similar to 'normal matter' for what its equation of state and coupling is concerned, "" We "know"? As far as I know, "dark Matter" is a ad hoc postulate to explain some problems in Cosmology concerning gravity. The surmised dark matter has to act "normal" to gravity, in all other respects it should be as undetectable as possible. So, in case that dark matter exists, it will act to gravity waves as normal matter does. –  Georg Jun 3 '11 at 9:10
@Georg - While I agree with your skepticism, the amount of evidence for something like dark matter is mounting higher and higher. Gravitational lensing studies are the most concrete evidence I know, particularly the gravitational lensing near galaxies that have recently collided. Their dark matter halos behaved significantly differently from the visible matter, differently in a manner that suggested some sort of mass that interacts only through gravity. So while its existence is questionable, I don't think its as questionable as all that. –  Omnifarious Jun 4 '11 at 16:40
I corrected my use of terminology. :-) –  Omnifarious Jun 4 '11 at 16:41
Well, if dark matter doesn't exist then it doesn't absorb gravitational waves either. My reply is referring to the usual LamdaCDM model & the contsraints we get from that on the nature of dark matter. I've omitted details simply because that wasn't the question. –  WIMP Jul 20 '11 at 9:40

To start this discussion I present a few facts about gravity waves. A weak linear gravity wave is a perturbation on a background metric $\eta_{ab}$ with the total metric $$g_{ab}~=~\eta_{ab}~+~h_{ab}.$$ The Ricci curvature to first order is $$R_{ab}~=~{1\over 2}\Big(\partial_c\partial_a{h^c}_b~+~\partial_c\partial_b{h^c}_a~-~\partial_a\partial_bh~-~\partial_c\partial^ch_{ab}\Big).$$ The harmonic gauge $\partial_c{h^c}_a~=~1/2\partial_a h$ gives the Einstein field equation $$\partial^c\partial_ch_{ab}~-~\frac{1}{2}\eta_{ab}\partial^c\partial_ch~=~\frac{16\pi G}{c^4}T_{ab},$$ for the traceless metric term ${\bar h}_{ab}~=~h_{ab}~-~(1/2)\eta_{ab}h$ with the simple wave equation $$\partial^c\partial_c{\bar h}_{ab}~=~\frac{16\pi G}{c^4}T_{ab}.$$

This gravity wave interacts with a set of test masses by inducing a quadrupolar motion. Let us suppose we have two such masses. These masses are on independent geodesics which will deviate from each other according to the variation of a vector connecting the masses $x^a$ by the equation $$\frac{d^2x^a}{ds^2}~=~{R^a}_{bcd}X^cU^bU^d.$$ For weak gravity we can set $U^b~\simeq~(1,~0,~0,~0)$, a pure time directed 4-vector and the geodesic deviation equation is approximately $$\frac{d^2x^a}{ds^2}~\simeq~{R^a}_bX^b.$$ One can then as an exercise input the Ricci curvature into this equation. Now let us assume there is a connecting spring between the two masses so that $$\frac{D^2x^a}{ds^2}~\simeq~\frac{d^2x^a}{ds^2}~-~{R^a}_bX^b,$$ where now the equation describes a deviation between two nongeodesic moving particles. Since the perturbing force is a spring we then have $D^2x^a/ds^2~=~-kx^a$, which is just the spring equation familiar from Newton’s second law of motion.

To address this question about dark matter interacting with gravity waves we think of this spring as the mutual interaction between particles. The spring constant for DM is very small, for DM is extremely weakly interacting. The result is that any heat which might be generated by gravity waves, $E~=~(3/2)\langle kx^2\rangle$ $=~kT$ will be very small. So using DM as a way of detecting gravity waves will likely prove to be frustrating.

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This is interesting. Unfortunately, the number of symbols and equations involved mean I would have to spend several days (and many google searches) in order to understand it. –  Omnifarious Jun 4 '11 at 16:44